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Proof step 471 from proof fsync-pages-keep-abs (previous step)

# buf = VFS_PAGE_SIZE, icache[ino].inode = mkinode(m3, md0, boolvar, m4, m5, m6), pcache[datakey(m, n)] = mkpentry(true, buf), files0[m] = mkfile(m0, md, m1, content), ((files0 ⊕ pcache) ⊕ icache)[ino] = ((files1 ⊕ pcache0) ⊕ icache)[ino], n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), m ∈ files0, datakey(m, n) ∈ pcache, ino ∈ files1, ino ∈ files0, ⌊err0⌋ ⊦ ((files1 ⊕ pcache0) ⊕ icache)[ino] = ((files0[m, mkfile(m0, md, m1, content[n, buf])] ⊕ pcache) ⊕ icache)[ino], ino ∈ icache ∧ ¬ boolvar

Heuristic elimination applied rule insert elim lemma

And obtained the following new goals

Proof step 472:
# buf = VFS_PAGE_SIZE, ((files0 ⊕ pcache) ⊕ icache)[ino] = ((files1 ⊕ pcache0) ⊕ icache)[ino], files0[m] = mkfile(m0, md, m1, content), pcache[datakey(m, n)] = mkpentry(true, buf), icache[ino] = mkientry(boolvar0, inode), inode = mkinode(m3, md0, boolvar, m4, m5, m6), n * VFS_PAGE_SIZE < m2, pcache-cons(pcache0, dirs, files1), ino ∈ files0, ino ∈ files1, datakey(m, n) ∈ pcache, m ∈ files0, ⌊err0⌋ ⊦ ((files1 ⊕ pcache0) ⊕ icache)[ino] = ((files0[m, mkfile(m0, md, m1, content[n, buf])] ⊕ pcache) ⊕ icache)[ino], ino ∈ icache ∧ ¬ boolvar

Rule argument

spec: icache-entry name: elim seq: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode) subst: [ie, boolvar, inode] → [icache[ino], boolvar0, inode]

Additional information

Used simplifier rules: ⊦ (boolvar ↔ ie.dirty) ∧ inode = ie.inode ↔ ie = mkientry(boolvar, inode); (elim) Used terms: icache[ino], boolvar0, inode